Least Common Multiple of 1968 and 1975

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1968 and 1975 the smallest integer that is 3886800 that is divisible by both numbers.

Least Common Multiple (LCM) of 1968 and 1975 is 3886800.

LCM(1968,1975) = 3886800

LCM of 1968 and 1975

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 1968 and 1975

LCM of 1968 and 1975 is 3886800

Least common multiple can be found by multiplying the highest exponent prime factors of 1968 and 1975. First we will calculate the prime factors of 1968 and 1975.

Prime Factorization of 1968


2 1968
2 984
2 492
2 246
3 123
41 41
1

Prime factors of 1968 are 2, 3,41. Prime factorization of 1968 in exponential form is:

1968 = 24×31×411

Prime Factorization of 1975


5 1975
5 395
79 79
1

Prime factors of 1975 are 5,79. Prime factorization of 1975 in exponential form is:

1975 = 52×791

Now multiplying the highest exponent prime factors to calculate the LCM of 1968 and 1975.

LCM(1968,1975) = 24×31×52×411×791
LCM(1968,1975) = 3886800

Factors of 1968

List of positive integer factors of 1968 that divides 1968 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 41, 48, 82, 123, 164, 246, 328, 492, 656, 984, 1968

Factors of 1975

List of positive integer factors of 1975 that divides 1975 without a remainder.

1, 5, 25, 79, 395, 1975

Least Common Multiple of 1968 and 1975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1968 and 1975, than apply into the LCM equation.

GCF(1968,1975) = 1
LCM(1968,1975) = ( 1968 × 1975) / 1
LCM(1968,1975) = 3886800 / 1
LCM(1968,1975) = 3886800

Properties of LCM 1968 and 1975

(i) The LCM of 1975 and 1968 is associative

LCM of 1968 and 1975 = LCM of 1975 and 1968

Related Least Common Multiples of 1968

Related Least Common Multiples of 1975

Frequently Asked Questions on LCM of 1968 and 1975

1. What is the LCM of 1968 and 1975?

Answer: LCM of 1968 and 1975 is 3886800.

2. What are the Factors of 1968?

Answer: Factors of 1968 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 41, 48, 82, 123, 164, 246, 328, 492, 656, 984, 1968. There are 20 integers that are factors of 1968. The greatest factor of 1968 is 1968.

3. What are the Factors of 1975?

Answer: Factors of 1975 are 1, 5, 25, 79, 395, 1975. There are 6 integers that are factors of 1975. The greatest factor of 1975 is 1975.

4. How to Find the LCM of 1968 and 1975?

Answer:

Least Common Multiple of 1968 and 1975 = 3886800

Step 1: Find the prime factorization of 1968

1968 = 2 x 2 x 2 x 2 x 3 x 41

Step 2: Find the prime factorization of 1975

1975 = 5 x 5 x 79

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 3886800 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 41 x 79

Step 4: Therefore, the least common multiple of 1968 and 1975 is 3886800.